There are two types of vehicle bearing apparatus, one for a drive wheel and one for a driven wheel. Especially in vehicle bearing apparatus that rotatably supports a wheel relative to a suspension apparatus, they are not only required to be made at a low cost but be light weight as well as small size to improve fuel consumption. A representative example of a prior art bearing apparatus for a vehicle driven wheel is shown in FIG. 6.
The bearing apparatus is a so called “third generation” and has a wheel hub 51, an inner ring 52, an outer ring 53, and double row rolling elements 54, 54. The wheel hub 51 has an integrally formed wheel mounting flange 55 at one end. An inner raceway surface 51a and an axially extending portion 51b, extending axially from the inner raceway surface 51a, are also formed on the wheel hub. Hub bolts 56 secure a wheel on the flange 55 and are equidistantly arranged along the periphery of the flange 55.
The inner ring 52 is formed with an inner raceway surface 52a on its outer circumferential surface. The inner ring 53 is press-fit onto the axially extending portion 51b of the wheel hub 51. The inner ring 52 is axially immovably secured to the wheel hub 51, by a caulked portion 51c, to prevent it from falling off of the axially extending portion 51b. The caulked portion 51c is formed by radially outwardly plastically deforming the end portion of the axially extending portion 51b. 
A body mounting flange 53b is integrally formed on the outer circumferential surface of the outer ring 53. The outer ring 53 includes double row outer raceway surfaces 53a, 53a on its inner circumferential surface. Double row rolling elements 54, 54 are freely rollably held between the outer raceway surfaces 53a, 53a and the opposing inner raceway surfaces 51a, 52a. 
The wheel hub 51 is made of carbon steel including carbon of 0.40˜0.80% by weight. The wheel hub 51 is formed with a hardened layer (shown by cross-hatching) in a region from the base of the wheel mounting flange 55 to the axially extending portion 51b through the inner raceway surface 51a. The hardened layer is formed by high frequency induction hardening. The caulked portion 51c remains as its original surface hardness after its forging. The inner ring 52 is made of high carbon chrome bearing steel such as SUJ2 and is hardened to its core by quenching.
Thus, it is possible to realize a vehicle wheel bearing apparatus with low cost which has sufficient durability to prevent damage such as cracks on the caulked portion 51c. Also, the apparatus prevents the generation of a large change in the diameter of the inner ring 52 secured on the wheel hub 51 by the caulked portion 51c. Also, it is possible to reduce the potential of the inner ring 52 from being damaged by the securing work to maintain the preload at an appropriate value. Also, this reduces the number of parts and steps of machining and assembly (see Japanese Laid-open Patent Publication No. 129703/1999).
However, in the bearing apparatus of the prior art, it is impossible to prevent generation of hoop stress in the outer diameter portion 57 of the inner ring 52. This is due to the inner diameter of the inner ring 52 being radially outwardly expanded due to the radially outward plastic deformation of the axially extending portion 51b near the caulked portion 51c during formation of the caulked portion 51c. 
It has been proposed, in order to reduce the hoop stress, to suppress the amount of plastic deformation during caulking by changing the configuration of the end portion of the axially extending portion 51b of the wheel hub 51. However, since the caulked portion 51c is required to have strength sufficient only to strongly secure the inner ring 52, even if a large momentum load is applied to the bearing apparatus, a conflicting problem, suppressing the amount of plastic deformation as well as ensuring the strength of the caulked portion, must be simultaneously solved.
When hoop stress is caused in the outer diameter portion 57 of the inner ring 52 and rust is generated in this portion, diffusible hydrogen exists and these circumstances would penetrate into the material of the inner ring 52 destroying its metal grain boundary. Thus, a so-called “delayed fracture” could be caused.
Several methods to measure the hoop stress have been developed. One method is to irradiate X-ray on the outer diameter portion 57 of the inner ring 52 in which maximum hoop stress occurs. Another method is to stick a strain gauge on the outer circumferential surface of the inner ring 52. However, neither method is simple and efficient when considered for use in a mass production process.